Question: Find the slope and y-intercept of the line that is ${\text{perpendicular}}$ to $\enspace {y = -x - 4}\enspace$ and passes through the point ${(-3, 6)}$. {1} {2} {3} {4} {5} {6} {7} {8} {9} {\llap{-}2} {\llap{-}3} {\llap{-}4} {\llap{-}5} {\llap{-}6} {\llap{-}7} {\llap{-}8} {\llap{-}9} {1} {2} {3} {4} {5} {6} {7} {8} {9} {\llap{-}2} {\llap{-}3} {\llap{-}4} {\llap{-}5} {\llap{-}6} {\llap{-}7} {\llap{-}8} {\llap{-}9}
Explanation: Lines are considered perpendicular if their slopes are negative reciprocals of each other. The slope of the blue line is ${-1}$ , and its negative reciprocal is ${1}$ Thus, the equation of our perpendicular line will be of the form $\enspace {y = x + b}\enspace$ We can plug our point, $(-3, 6)$ , into this equation to solve for ${b}$ , the y-intercept. $6 = -3 + {b}$ $6 + 3 = {b} = 9$ The equation of the perpendicular line is $\enspace {y = x + 9}\enspace$. ${m = 1, \enspace b = 9}$